HAVANA — President Obama stood beside President Raúl Castro on Monday and declared a “new day” of openness between the United States and Cuba, but old grievances and disputes over human rights marred a groundbreaking meeting and underscored lingering impediments to a historic thaw.

The two presidents, meeting at the Revolutionary Palace for the first such official contact between their two governments in more than a half-century, engaged in a frank and at times awkward exchange with each other and reporters. Mr. Obama at turns prodded Mr. Castro to submit to questions during an extraordinary 55-minute news conference.

Standing at lecterns in a cavernous granite-walled hall in front of Cuban and American flags, the two leaders traded criticism of each other’s countries even as both said they were committed to continuing on the path to normalizing relations.

“Give me a list of the political prisoners and I will release them immediately,” Mr. Castro said, asked by a reporter about dissidents his government has arrested. “Just mention the list. What political prisoners?”

Human rights groups quickly produced rosters, distributed over email and social media, of people they said had been imprisoned in Cuba for demonstrating against or otherwise challenging Mr. Castro’s government.

Mr. Castro sought to turn the human rights criticism on the United States, arguing that countries that do not provide universal health care, education and equal pay are in no position to lecture Cuba. He also said the United States military base at Guantánamo Bay should be returned to Cuba.

“It’s not correct to ask me about political prisoners,” Mr. Castro said.

Mr. Obama said he had pressed the Cuban president in their meeting over Cuba’s treatment of dissidents and reaffirmed that he would meet with some dissidents privately on Tuesday. But he also assured Mr. Castro that the United States had no intention of dictating his country’s future.

“I affirm that Cuba’s destiny will not be decided by the United States or any other nation,” Mr. Obama said. “Cuba is sovereign and rightly has great pride, and the future of Cuba will be decided by Cubans, not by anybody else.”

The president went a step further, in comments likely to be seized upon by critics of his push to pursue an opening with Cuba, conceding that the United States must face up to the criticisms Mr. Castro unleashed.

“I actually welcome President Castro commenting on some of the areas where he feels that we’re falling short, because I think we should not be immune or afraid of criticism or discussion as well,” Mr. Obama said.

The apparent rapport between the two presidents at the news conference was a striking display of warmth on a day that was dominated by the symbolism of the first tentative openings between Cuba and the United States since the Cold War.

Mr. Obama said he expected to see the lifting of the United States’ trade embargo of Cuba, something Mr. Castro called “the most important obstacle to our economic development and the well-being of the Cuban people.”

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Amid the euphoria of President Obama’s visit is a darker reality for the artist Danilo Maldonado Machado, who has been jailed for his work. He hopes this week will spotlight Cuba’s repression.CreditCreditLisette Poole for The New York Times

“We agree that a long and complex path still lies ahead,” Mr. Castro said, smiling warmly at Mr. Obama at times, even when the American president teased his Cuban host about the Castro family’s penchant for stem-winding speeches. “What is most important is that we have started taking the first steps to build a new type of relationship, one that has never existed between Cuba and the United States.”

There were awkward moments as well, with both presidents pushing each other outside their comfort zones. Mr. Obama, who was determined to mark the occasion with a news conference — something Mr. Castro seldom if ever does — prodded the Cuban leader to submit to journalists’ questions.

After Mr. Obama finished answering a question from Andrea Mitchell, the NBC News correspondent, he urged Mr. Castro to do so as well.

“It’s up to you,” Mr. Obama told Mr. Castro. “She’s one of our most esteemed journalists in America, and I’m sure she’d appreciate just a short, brief answer.”

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Cubans crowded the streets of Havana on Sunday to try to catch a glimpse of President Obama and his family.CreditStephen Crowley/The New York Times

Mr. Castro did answer Ms. Mitchell’s query about human rights, scolding her that the question was unfair.

After the news conference, the two men joined hands in what appeared to be a cross between a handshake and the raising of a revolutionary fist; Mr. Obama held out his arm awkwardly and it ended up as neither.

Mr. Obama began his day at the memorial to the Cuban journalist and poet José Martí, whose ideals are invoked with zeal in Miami and Havana.

A Cuban military band played “The Star-Spangled Banner” under a billowing Cuban flag as the American president and a Cuban Politburo member appeared side by side, flanked in the distance by huge sculptured portraits of Che Guevara and Camilo Cienfuegos, the revolutionaries who were intimates of Fidel Castro.

During his carefully stage-managed visit this week, Mr. Obama does not plan to meet with Fidel Castro, 89, the former president, who is Raúl’s older brother.

But he said in an interview with ABC News on Monday that he would be “happy” to meet at some point with the elder Mr. Castro. “If his health was good enough that I could meet with him, I’d be happy to meet with him, just as a symbol of the end of the — or the closing of this Cold War chapter in our mutual histories,” Mr. Obama said.

In Havana on Monday, many Cubans still seemed uncertain about whether they had permission to try to see Mr. Obama, never mind express a point of view. Cubans all over the city seemed to be constantly asking where Mr. Obama would be.

In Parque Central in Havana, Mr. Obama’s visit touched off talk of politics, freedom, race and the scene of an American president at Revolution Plaza near an image of Guevara.

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President Obama and President Raúl Castro at the Revolutionary Palace in Havana on Monday.CreditPablo Martinez Monsivais/Associated Press

“I see the Cubans in the United States talking bad about Obama because he was standing with the image of Che behind him,” said Alfredo Calderon, 83, a retired musician who now works as a custodian. “I don’t see it as bad.”

He continued: “I have to admit, I am 83 years old, and I have seen a lot happen. I did not think I would see that.”

In a nation that stifles dissent, the men in the square were quick to shout out the kinds of things they hope Mr. Obama will bring to Cuba. “Freedom of speech!” one man shouted. “Freedom of expression!” another echoed.

“We want change,” said Angel Maturrell, a small-business owner. “Change. Change. Change. All kinds. Any kind. We are tired of waiting.”

A few blocks away, Cubans and foreigners found themselves running into American lawmakers and V.I.P.s touring the city.

Senator Patrick J. Leahy of Vermont was spotted by the cathedral; Representative Charles B. Rangel of New York was also easy to find. Wearing a seersucker suit and a Tampa Bay Rays baseball cap, Mr. Rangel said he could not have been happier. He spent decades in Congress working to end the embargo.

He said he was confident that restored relations would yield benefits for both nations.

“I never knew we could bring such a crack in the wall,” Mr. Rangel said. “We’re creating the right conditions for when change really comes.”

A version of this article appears in print on , on Page A1 of the New York edition with the headline: A ‘New Day’ of Openness, Taxed by Old Grievances. Order Reprints | Today’s Paper | Subscribe